On the convergence of the Newton-GMBACK method

Abstract

When the GMBACK solver is used in the Newton iterates, the iterates may be written either as inexact Newton iterates or as quasi-Newton iterates. In this paper present results which assure the local convergence of the iterates in the both settings.

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Keywords

linear systems; Krylov solvers; GMBACK; backward error.

Cite this paper as:

E. Catinas, On the convergence of the Newton-GMBACK method. 2007 International Conference on Engineering and Mathematics, Bilbabo, July 9-11, 2007, pp.11-14.

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[1 E. Catinas,  Inexact perturbed Newton methods and applications to a class of Krylov solvers,  I. Optim. Theory, Appl. 108 (2001), 543-570.

[2] E. Catinas,  On the superlinear convergence of the successive approximations method,  J. Optim. Theory Appl., 113 (2002), 473-485.

[3] E. Catinas,  The inexact perturbed and quasi-Newton methods are equivalent models, Math. Comp., 74 (2005), no. 249, pp. 291-301.

[4] R. S. Dembo, S.C. Eisenstat and T. Steihaug,  Inexact Newton methods, SIAM, J. Numer. Anal. 19 (1982), 400-408.

[5] J. E. Dennis, Jr. and J. J. More,  A characterization of superlinear convergence and its application to quasi-Newton methods,  Math. Comp. 28 (1974), 549-560.

[6] E. M. Kasenally, GMBACK: a generalised minimum backward error algorithm for nonsymmetric linear system, SIAM J. Sci. Comput. 16 (1995), 698-719.

[7] E. M. Kasenally and V. Simoncini,  Analysis of a minimum perturbation algorithm for nonsymmetric linear systems, SIAM J. Numer. Anal. 34 (1997), 48-66.

[8] B. Morini, Convergence behaviour of inexact Newton methods, Math. Comp. 68 (1999), 1605-1613.

[9] J. M. Ortega and W. C. Rheinboldt, Iterative Solution of Nonlinear Equations in Several Variables, Academic Press, New York, 1970.

[10] F. A. Potra, On Q-order and R-order of convergence, J. Optim. Theory Appl. 63 (1989), 415-431.

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